Internal problem ID [5318]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary
problems. Page 39
Problem number: 23 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {x^{2} \cos \left (y\right ) y^{\prime }-2 x \sin \left (y\right )=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*cos(y(x))*diff(y(x),x)=2*x*sin(y(x))-1,y(x), singsol=all)
\[ y \left (x \right ) = -\arcsin \left (\frac {3 c_{1} x^{3}-1}{3 x}\right ) \]
✓ Solution by Mathematica
Time used: 10.185 (sec). Leaf size: 21
DSolve[x^2*Cos[y[x]]*y'[x]==2*x*Sin[y[x]]-1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arcsin \left (\frac {1}{3 x}+2 c_1 x^2\right ) \]